相关论文: An Infinitary Proof Theory of Linear Logic Ensurin…

Initiated by Abramsky [1994], the Proofs as Processes agenda is to establish a solid foundation for the study of concurrent languages, by researching the connection between linear logic and the $\pi$-calculus. To date, Proofs as Processes…

We introduce an infinitary first order linear logic with least and greatest fixed points. To ensure cut elimination, we impose a validity condition on infinite derivations. Our calculus is designed to reason about rich signatures of…

Client-server sessions are based on a variation of the traditional interpretation of linear logic propositions as session types in which non-linear channels (those regulating the interaction between a pool of clients and a single server)…

We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…

Infinitary and cyclic proof systems are proof systems for logical formulas with fixed-point operators or inductive definitions. A cyclic proof system is a restriction of the corresponding infinitary proof system. Hence, these proof systems…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

Termination is a central property in sequential programming models: a term is terminating if all its reduction sequences are finite. Termination is also important in concurrency in general, and for message-passing programs in particular. A…

Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a…

The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…

We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…

We study a theory of asynchronous session types ensuring that well-typed processes terminate under a suitable fairness assumption. Fair termination entails starvation freedom and orphan message freedom namely that all messages, including…

We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent…

A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…

The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…

Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…

There exists a broad family of multiparty sessions in which the progress of one session participant is not unconditional, but depends on the choices performed by other participants. These sessions fall outside the scope of currently…

We present a sequent calculus system for a modal reformulation of a system of nonmonotonic logic due to McCain and Turner: we prove cut elimination for our system. The proof system is in general infinitary: because we can prove cut…